This invention relates generally to apparatus and methods useful for changing the state vector of a space object when the space object is moving relative to a magnetic field. More specifically, the present invention relates to an apparatus and method of using a conducting tether to produce an electrodynamic force to change the orbit of a satellite around a celestial body, such as the Earth, which has an associated magnetic field, and still more specificly to deorbit a satellite from its orbit.
The present invention has its principal utility in outer space, primarily for changing the state vector of a space object, for example deorbiting satellites at the end of their useful life to mitigate the harm and reduce the liability created by the proliferation of space debris. In order to obtain a better understanding of the present invention it is helpful to understand the prior art of space tethers, especially tether dynamics and tether electrodynamics. The present invention may be more readily understood through a review of the experimental prior art and a mathematical analysis of electrodynamic space tethers.
Prior Art Tethers
A tether was originally a rope or chain used to fasten an animal so that it grazed only within certain limits. Tethers have been used for decades in space to attach astronauts to their spacecraft.
In 1974 Professor Guiseppe Colombo, holder of the Galileo chair of astronomy at the University of Padua in Italy, proposed using a long tether to support a satellite from an orbiting platform. U. S. Pat. No. 4,097,010, which issued to Professor Colombo and Mario Grossi on June 27, 1978, teaches a satellite connected by means of a long tether to a powered spacecraft. Colombo actively pursued the design of a tethered satellite system.
Several NASA experiments, such as the two Small Expendable Deployer System (SEDS 1 and 2) experiments and the Plasma Motor Generator (PMG) experiment used tethers in space. SEDS used a nonconducting tether. The PMG used a 500-meter conducting tether. The Tethered Satellite System flights in 1992 and 1996 (TSS-1 and 1R) used a 20,000-meter conducting tether.
On the TSS-1 mission the tether deployed only 260 meters (853 feet) before the deployer failed. On the TSS-1R the tether was deployed 19,500 meters. In the SEDS-2 flight, a 0.8-mm diameter, 20,000-meter long braided single-line tether was deployed to study tether dynamics and lifetime. Orbital debris or a meteoroid severed this tether in less than four days.
In the TSS-1R flight, the conducting single-line tether was severed after five hours of deployment. This failure was caused by an electric arc produced by the 3,500 volts of electric potential generated by the conductive tether""s movement through the Earth""s magnetic field.
The Tether Physics and Survivability (TiPS) satellite consists of two end masses connected by a 4,000-meter long non-conducting tether. This satellite was deployed on Jun. 20, 1996 at an altitude of 1,022 kilometers (552 nautical miles). Its tether is an outer layer of Spectra(trademark) 1000 braid over a core of acrylic yarn. The yarn will xe2x80x9cpuffxe2x80x9d its outer braid to two millimeters to xe2x80x9cgive it a larger cross section to improve its resistance to debris and small micrometeoroidsxe2x80x9d, according to the National Reconnaissance Office (NRO), which is a sponsor of the TiPS mission. As of Jun. 21, 2000 the TiPS tether had survived four years.
1. Joseph A. Carroll, xe2x80x9cSEDS Deployer Design and Flight Performancexe2x80x9d, paper WSEDSA-1 at the 4th International Conference on Tethers in Space, Washington, DC, April 1995.
2. James E. McCoy, et. al. xe2x80x9cPlasma Motor-Generator (PMG) Flight Experiment Resultsxe2x80x9d, pp.57-84, Proceedings of the 4th International conference on Tethers in Space, Washington, DC, April 1995.
3. W. John Raitt, et.al. xe2x80x9cThe NASA.ASI-TSS-1 Mission, Summary of Results and Reflight Plans, pp. 107-118, Proceedings of the 4th International conference on Tethers in Space, Washington, DC, April 1995.
4. Joseph C. Anselmo, xe2x80x9cNRO Orbiting Spacecraft Studies Tether Survivabilityxe2x80x9d, Aviation Week, page 24, Jul. 1, 1996.
These experiments all used single line tethers.
The following reference is illustrative of the current state of the art in space tethers: Paul A. Penzo and Paul W. Ammann. Tethers in Space Handbookxe2x80x94Second Edition. NASA Office of Space Flight, NASA Headquarters, Washington, DC 20546. See also the hundreds of references in the 33 page bibliography at the end of the handbook.
The xe2x80x9cHoytetherxe2x80x9d(trademark), an Improved, High-Reliability Tether
In 1991, one of the present inventors, Robert Hoyt, invented a lightweight net-like structure that provides many redundant load-bearing paths. A number of primary load bearing lines running the length of the structure are connected periodically by diagonal secondary lines. The disclosed embodiment of this invention has the secondary lines firmly connected by knots to the primary lines. The secondary lines are connected only to the primary lines. At either end of the disclosed structure, a support ring enforces the cylindrical spacing between the primary lines. The secondary lines are designed with a small amount of slack. These secondary lines are only put under load if a primary line fails. This specific tether structure was disclosed to the public in 1992 (Forward, R. L., xe2x80x9cFailsafe Multistrand Tether Structures for Space Propulsionxe2x80x9d, AIAA paper 92-3214, 28th Joint Propulsion Conference, Nashville, Tenn., 1992 (hereinafter xe2x80x9c1992 Hoytether structurexe2x80x9d). This structure was named a xe2x80x9cHoytetherxe2x80x9d. The term xe2x80x9cHoytetherxe2x80x9d is used throughout the remainder of this specification for this type of tether structure.
The present invention uses an improved Hoytether, which was invented by the same inventors as the present invention. This improved Hoytether is the subject of a copending PCT application. The Hoytether is discussed briefly in this specification to aid understanding of the present invention.
The 1992 Hoytether design teaches that the normally slack secondary lines have half the cross-section (0.707 the diameter) of the primary lines. There are twice as many secondary lines as primary lines, thus the mass of the secondary lines is equal to the mass of the primary lines. In an undamaged Hoytether, the primary lines carry the entire load, while none of the secondary lines are under load.
While the survival probability of a single-line tether decreases exponentially with time, the Hoytether can maintain a high, i.e. greater than 99 percent, survival probability for periods of months or years (Forward and Hoyt, xe2x80x9cFailsafe Multiline Hoytether Lifetimesxe2x80x9d, Paper AIAA 95-2890, 31st Joint Propulsion Conference, July 1995).
1. Robert L. Forward, Failsafe Multistrand Tethers for Space Propulsion, Forward Unlimited, P.O. Box 2783, Malibu, Calif. 90265, July 1992, Final Report on NASA Contract NAS8-39318 SBIR 91-1 Phase I.
2. Robert L. Forward and Robert P. Hoyt, Failsafe Multistrand Tether SEDS Technology Demonstration, Final Report on NAS8-40545 with NASA/MSFC (Jun. 14, 1995).
3. Robert L. Forward and Robert P. Hoyt, xe2x80x9cHigh Strength-to-Weight Tapered Hoytether for LEO to GEO Payload Transferxe2x80x9d Final Report on contract number NAS8-40690 with NASA/MSFC (Jul. 10, 1996).
The Hoytether is essentially a tri-axial net structure, with xe2x80x98primaryxe2x80x99 lines running along the length of the tether and two sets of xe2x80x98secondaryxe2x80x99 lines connecting these primaries diagonally. They can be made by hand and connected with knots as is taught by the 1992 Hoytether structure. Because knotted connections severely limit the strength of a structure, it is desirable to use a knotless fabrication technique to achieve interconnections that have strengths approaching the limits of the constituent material. As these tethers may be many kilometers long; fast and inexpensive mechanical methods are required for their practical fabrication.
Hoytethers may be made by mechanical braiding, i.e. three-dimensional braiding, such as 3-D rotation braiding using braiding machines such as those developed by the Herzog Company in Germany (August Herzog Maschinenfabrik GmbH and Co., Postfach 2260.26012, Oldenburg, Germany. The specialized loom developed by the Nichimo Company of Japan (Nichimo Company Ltd., 2-6-2 Ohtemachi, Chiyoda-Ku, Tokyo, Japan) is used to produce xe2x80x9cUltracrossxe2x80x9d knotless fishing nets in which the individual strands are braided as a 4-braid line, and the strands are interbraided where they cross. This produces netting that has slipless interconnections that are very strong, approaching the maximum capability of the fiber. Such a loom could, with some modifications, produce the present invention""s structure. Only two such machines exist, one in Japan, the other in Washington State. Unfortunately neither can work with the small line diameters needed to practice the preferred embodiment of the present invention. See generally, Ko, F. K., xe2x80x9cBraidingxe2x80x9d, in Engineered Materials Handbook, Vol. 1., Composites. ASM International, Metals Park, Ohio, 1957. Pp. 519-528.
The most common 3-dimensional braiding machines are 4-step braiders based upon the designs of Maistre (German Patent P230-16986, issued 1973) and Forentine (U.S. Pat. 4,312,261, issued 1982). Braiding is accomplished by using pneumatics or solenoids to push the parts of the braiding machine to the proper positions. This is a slow process and making a Hoytether kilometers long with these machines would be very time consuming and expensive. The composites division of Albany International (Albany International Research Company, 777 West Street, Mansfield, Mass.) also produces a 3-D braiding machine. This machine uses modular braiding components that are assembled breadboard fashion on a large wall.
Although braiding is the preferred technique, alternate fabrication methods such as Raschel knitting and crocheting can be used successfully. Multikilometer long Hoyththers are presently being produced for the inventors by the vendors Culzean Fabrics and Flemings Textiles using an electronically controlled crochet machine produced by Comez in Italy.
Space Tether Systems
The prior art teaches the use of tethers in space applications. U.S. Pat. No. 5,163,641, issued on Apr. 9, 1990 to Yasaka, teaches the use of a powered spacecraft connected by a tether to a satellite. This tether is disconnected to change the state vector of the satellite. The state of the art of energy and momentum transfer using space tethers is discussed in Ivan Beckey""s article xe2x80x9cTethering, a new Technique for Payload Deploymentxe2x80x9d, Aerospace America, March 1997, at pages 36-40. Beckey concludes, xe2x80x9cTethers can perform the same functions as propulsive upper stages of direct payload injection, but at lower weight and cost per pound.xe2x80x9d U.S. Pat. 4,923,151, issued Mar. 1, 1988 to Roberts, Wilkinson and Webster, teaches a tether power generator for earth orbiting satellites. U.S. Pat. 4,580,747, issued Mar. 15, 1983 to Pearson, teaches use of a long tether extending downward into the atmosphere from a satellite. The state vector of the satellite is changed by forces acting on a lifting body connected to the end of the tether. U.S. Pat. 4,824,051, issued Jan. 12, 1987 to Engelking, teaches passing an electric current through a conductive tether attached to a satellite to provide propulsive force to alter the orbit of the satellite. U.S. Pat. 5,082,211, issued Jan. 21, 1992 to Werka, teaches use of a tether to deorbit space debris. U.S. Pat. 4,727,373, issued Mar. 31, 1986 to Hoover, teaches an orbiting stereo imaging radar system having two spacecraft in synchronous parallel orbits connected by a tether.
Tether Dynamics
In order to understand the forces that cause a tethered satellite to move upward and away from an orbiting satellite, for example, it is first necessary to explain briefly how a satellite remains in orbit. An orbiting satellite is acted on by the force of gravity, which pulls it toward Earth, and by a centrifugal force, which pushes it away from Earth. The centrifugal xe2x80x9cforcexe2x80x9d (actually inertia) results from the motion of the satellite around its circular orbit. This is the same force that one can experience by swinging a ball around on the end of a string. A satellite is maintained in its orbit when it travels at the natural speed for its altitude and, as a result, the centrifugal force is equal to the gravitational force.
At the typical orbital altitude of 250 kilometers for a low-Earth orbit satellite, for example, a speed of approximately 7.6-km per second is required to create sufficient centrifugal force to balance gravitational attraction on the satellite. If the altitude is changed, the two opposing forces will no longer be in balance unless the satellite also changes its speed. A higher orbital altitude requires a slightly lower speed so the satellite will take longer to complete an orbit. Because of this, if two free-flying satellites are in orbits at different altitudes, the lower satellite will circle the Earth in less time than the satellite in the higher orbit.
If two satellites, at different altitudes, are connected to each other by a tether, they are forced to travel around their orbits togetherxe2x80x94in the same period of time, which is longer than the natural period of the lower satellite but shorter than that of the upper satellite. The lower satellite will, therefore, slow down below the natural speed for its orbit and will tend to fall to a lower orbit because the centrifugal force will now be less than the gravitational attraction of the Earth. An upward force in the tether that makes up the difference between centrifugal and gravitational forces holds it in place, however.
Correspondingly, the upper satellite will be accelerated above its natural orbiting speed (increasing its centrifugal force above the gravitational attraction) and will tend to move to a higher orbit. It, too, is held in place by an additional force (downward) in the tether. In other words, the net force downward on the lower satellite is balanced, through the tether, by the net force upward on the upper satellite. The effect of unbalanced forces on the two satellites is, therefore, to create tension in the tether. During the TSS-1 and 1R experiments, the inertia of the tethered satellite causes the satellite to rise above the orbiter as the tether is reeled out. Very close to the orbiter, there is little difference in the two orbits, and the tension force is insufficient to overcome friction in the deployer mechanism; therefore, until the satellite reaches a separation of approximately 1000-meters, the tension is augmented by small tether-aligned thrusters on the satellite. Beyond this point, the tension in the tether is the only force required.
By experimenting with a ball hung on a piece of elastic cord (a paddleball, for example) it is possible to simulate all the different types of oscillations that are possible on a space-based tether system. The elastic cord, representing the tether, may compress and stretch, causing the ball to bounce up and down (longitudinal oscillation). It also may move in a circular (skip-rope) motion or may develop wave-like motions (transverse oscillations). Even if the string itself remains straight, it is possible to get the ball swinging back and forth about its attachment point on the paddle like a child on a swing rope (pendulous motion).
Each type of motion occurs with a particular frequency, which depends on the length and tension of the tether. When the frequencies are different, the motions do not interact; however, at some tether lengths, the frequencies of two or more types of oscillation can become very close. At this point, energy can be transferred from one type of motion to another, a phenomenon known as resonance. For instance, the transverse oscillations in the tether may cause the satellite to swing back and forth in pendulous motion.
Many different factors may cause oscillations; the movements of the satellite or Shuttle are but two of these. For an electrodynamic tether, the skip-rope and pendulous oscillations are of particular interest. If a current is passed through a tether, the current will interact with Earth""s magnetic field, resulting in a force that may produce skip-rope and pendulous oscillations. Because it is necessary to maintain control of the satellite, much study has gone into identifying the different types of possible motions and the methods used to control them.
One way to control the magnitude of those motions that cause a change in tension or transverse motion at the end of the tether is to have an end mass connected to the Hoytether that maintains a controlled tension on the tether, working much like a spring-loaded xe2x80x98dog leashxe2x80x99. This may be as simple as a coiled spring, or as complex as an active control system that measures the tension and transverse forces on the tether and adjusts the applied tension according to a local or remotely operating algorithm.
Electrodynamic Effects of Conductive Tethers
Electric potential is generated across a conductive tether by its motion through the Earth""s magnetic field. Electromagnetic forces acting on a conductive tether in orbit can make the tether system behave like an electric motor or generator, thereby exerting a useful force to alter the state vector of the tether and any mass attached to it.
Electrodynamic tether propulsion is unlike most other types of space propulsion in use or being developed for space application todayxe2x80x94there is no hot gas expelled to provide thrust. Instead, the environment of near-Earth space is being utilized to propel a spacecraft or upper stage via electrodynamic interactions.
A charged particle moving in a magnetic field experiences a force that is perpendicular to its direction of motion and the direction of the field. When a current flows through a long, conducting tether the electrons flowing through the tether experience this force due to the fact that they are moving along the wire in the presence of Earth""s magnetic field. The current induced force is perpendicular to the tether. This force is transferred to the tether and to whatever the tether is attached (like a spacecraft, satellite, space station or upper stage). It can be an orbit-raising thrust force or orbit- lowering drag force, depending upon the direction of current flow. Operation in one mode allows boost from LEO to higher orbit while reversing the current flow provides negative thrust for deboost. The principle is much the same for an electric motor; reverse its operation and it acts as a generator. Current is obtained from the ionosphere with collection and emission occurring on opposite ends of the tether.
The PMG experiment demonstrated that a conducting tether can be used as both a motor and a generator. The TSS experiments, specifically TSS-1R, showed that very large voltages (about 3500 volts) can be generated by a sufficiently long tether.
Uses of an electrodynamic tether as its orbit raising and lower propulsion system has many advantages over competing systems:
a. It is nearly propellantless. Most other systems expel hot gases and require extensive resupply. To emit current, the electrodynamic tether propulsion system will likely use plasma contactors developed as a part of the International Space Station Program. These contactors consume less than 20 kg of xenon gas per year with a 50% duty cycle.
b. It can change both altitude and inclination. The Earth""s magnetic field is non-uniform and can therefore provide both in- and out-of-plane forces for inclination changes as well as altitude changes. This is of particular interest to payloads requiring polar orbits in that they can be launched on a small launch vehicle into a lower inclination orbit and have it raised in space by the proper phasing of current through the tether.
A demonstration of the propulsive capabilities of electrodynamic tethers was recently approved for flight in 1999. The Propulsive SEDS mission, or ProSEDS, will fly as a secondary payload on a Delta II launch vehicle and deploy a 5-km conducting tether using the existing SEDS deployer concept. The ProSEDS experiment will be followed by the Electrodynamic Tether Upper Stage (EDTUS) experiment that will demonstrated the use of electrodynamic forces to change both the altitude and inclination of the experimental spacecraft. FIGS. 1b and 1c show, respectively, the calculated electrodynamic thrust at several inclinations and the reentry time sensitivity of the ProSEDS tether.
One application for long-life conducting electrodynamic tethers with is as a xe2x80x9cTerminator Tether(trademark)xe2x80x9d for removing from orbit, unwanted Earth orbiting spacecraft at the end of their useful lives. When the mission of the satellite is completed, the Terminator Tether(trademark), weighing a small fraction of the mass of the satellite, would be deployed. The electrodynamic interaction of the conducting tether with the Earth""s magnetic field will induce current flow in the tether conductor. The resulting energy loss from the heat generated by the current flowing through the ohmic resistance in the conducting tether will remove energy from the spacecraft, eventually causing it to deorbit, thus reducing the amount of orbital space debris that must be coped with in the future.
In 1995, M. Grossi presented a paper published in the Proceedings of the 4th International Conference on Tethers in Space. In two paragraphs he briefly mentions the use of tethers as an xe2x80x9cemergency brakexe2x80x9d for a spacecraft. However, Grossi""s article contains no details of either the mechanism or the method by which this could be accomplished.
In the following analysis, it is shown that the amount of energy loss generated by an electrodynamic tether is essentially independent of its length or area, and instead is primarily proportional to the tether mass and the physical properties of the conductor metal chosen. In the typical example calculated, a 1000-kg spacecraft can be deorbited from a 1000-km high Earth orbit by a 10-kg mass tether in a month, while a 1-kg tether can deorbit a 1000-kg spacecraft in less than a year.
To the knowledge of the inventors, Joseph P. Loftus of NASA/JSC first proposed the general concept of using an electrodynamic tether to deorbit spent satellites. In order to show that the Loftus deorbit concept was not obvious to those skilled in the art of electrodynamic tethers one of the present inventors, Forward contacted the leading expert on space tethers, Joseph Carroll, of Chula Vista, Calif., who built and participated in the flight test of the PGM. After being told of the Loftus concept in a telephone conversation, his reply in an Email message dated August 5, 1996, was xe2x80x9csuch a system would be feasible . . . by it is still not obvious to me that it would be useful . . . xe2x80x9d
Loftus was considering the use of electrodynamic drag from a conducting tether to achieve this goal of bringing the unwanted spacecraft down from its high orbit (where atmospheric drag is negligible) to a 200-km orbit, where atmospheric drag would rapidly finish off the task of removing the unwanted spacecraft from orbit. The tether Loftus was considering was a single-line, conducting tether, typically 1-mm in diameter, 1-km long, and, if made of aluminum, 2-kg in mass. He would include means at the ends of the tether to contact the ambient space plasma around the Earth to complete the current loop.
Unfortunately it is probable that space impactors would sever the 1-mm diameter, 1-km long single-line tether proposed by Loftus within a 1/e lifetime of four months. This would produce orbital debris rather than removing it. The motivation for this work is the NASA Safety Standard NSS 1740.14 xe2x80x9cGuidelines and Assessment Procedures for Limiting Orbital Debris.xe2x80x9d The relevant portion of the Standard starts on page 6-3: General Policy Objectivexe2x80x94Postmission Disposal of Space Structures. Item 6-1: xe2x80x9cDisposal for final mission orbits passing through LEO: A spacecraft or upper stage with perigee altitude below 2000 km in its final orbit will be disposed of by one of three methods.xe2x80x9d The method of interest is the atmospheric reentry option, Option a: xe2x80x9cLeave the structure in an orbit in which, using conservative projections for solar activity, atmospheric drag will limit the lifetime to no longer than 25 years after completion of mission. If drag enhancement devices are to be used to reduce the orbit lifetime, it should be demonstrated that such devices will significantly reduce the area-time product of the system or will not cause the spacecraft or large debris to fragment if a collision occurs while the system is decaying from orbit.xe2x80x9d
The NASA standard applies only to NASA spacecraft and even then only to completely new spacecraft designs. New versions of existing designs are to make a xe2x80x9cbest effortxe2x80x9d to meet the standard, but will not be required to change their design to do so. The Department of Defense has adopted the NASA standard with the same provisos. An Interagency Group report has recommended that the NASA standard be taken as a starting point for a national standard. It is NASA""s recommendation to the Interagency Group that the safety requirement be phased in only as spacefaring nations reach consensus internationally, which is being done through the International Debris Coordination Working Group whose members are Russia, China, Japan, ESA, UK, India, France, Italy, and the US.
Thus, although the NASA Safety Standard in its present form is not the xe2x80x9cLawxe2x80x9d, the existence of the standard means that some time in the future a similar requirement may be imposed on all spacecraft. This could result in major growth in future space tether business, with a sale to every non-geostationary spacecraft being xe2x80x9cmandatedxe2x80x9d by government safety regulations, somewhat as the sale of seat belts and airbags for every car are mandated.
In fact, three of the companies planning to set up xe2x80x9cconstellationsxe2x80x9d of low to medium orbit communications: Teledesic, Iridium and Odessey have have committed their companies to abide by the spirit of NASA Safety Standard 1740.14 by using one means or another to deorbit their spacecraft fefore they reach end of life.
Problems with Prior Art Tethers
All electrodynamic tether designs proposed by the prior art teach that the tether should be operated at a right angle to the magnetic field through which the tether is moving and moving in a direction that sweeps across the largest area of magnetic field lines. When the magnetic field is horizontal to the surface of the Earth, as is near the equator, this is accomplished by having the tether length vector oriented along the local vertical or perpendicular to the direction of spacecraft motion, the state vector of the spacecraft. This is a problem because the electrodynamic force acting on the tether causes the tether to align itself with the state vector of the spacecraft rather than perpendicular to it. To overcome this problem the prior art teaches the use of a large ballast mass attached to the end of the tether and/or use of a very long (tens to hundreds of kilometers) tether. The large ballast mass is expensive to take to orbit because it replaces useful payload. The long tether sweeps a larger Area-Time-Product during its useful life and thus is more likely to impact other space objects, either debris or another spacecraft.
Another problem common to all proposed prior art tethers is tether instability. If the tether produces a large electrodynamic drag force, which is desirable because a large drag force will cause the satellite to deorbit quickly, then the tether will be dynamically unstable. This instability can cause the tether to lose its effectiveness, act uncontrollably and even wrap around the satellite or otherwise malfunction. Experts skilled in the art of tether design have opined that this dynamic instability is inherently unavoidable in any electrodynamic tether system. The prior art solution, such as that presently being used in the ProSEDS experiment, has been to use a large ballast mass to increase the stabilizing gravity-gradient force and/or to limit the electrodynamic drag of the tether to less that the maximum that could be produced. In the ProSEDS experiment, the conducting electrodynamic tether is five kilometers long. To insure stability, it will be augmented by a 20-35 kilometer long non-conducting tether, which to further have stability will have a 40 kilogram ballast end mass.
Yet another problem of all proposed prior art electrodynamic tether systems is how to radiate away the energy produced by the tether""s operation. A satellite moving at an orbital velocity of 18,000 miles per hour has a kinetic energy of over 10,000 calories per gram. To put this amount of energy in an understandable perspective, it may be noted that when nitroglycerine explodes it produces about 1,500 calories per gram. Prior art designs of electrodynamic drag tethers teach the use of the electrical energy generated by the tether to charge batteries or operate electronics, with the excess energy being converted into heat by a resistive load. This excess heat must be radiated to the space environment or it will melt the resistive load. Thus the resistive load, and/or its associated radiator structures, must be massive and replace useful payload.
The present invention comprises an electrodynamic tether structure and a method of use. The principal industrial utility of the present invention is to deorbit satellites in Earth orbit at the end of their useful life. This embodiment of the present invention is sometimes referred to in this specification as a xe2x80x9cTerminator Tether(trademark)xe2x80x9d because it terminates the orbital lifetime of the host spacecraft. The structure of the tether taught by the present invention is a short, wide (compared to the long single wires of the prior art) conductive Hoytether whose area maximizes electrodynamic drag while simultaneously minimizing the Area-Time-Product swept by the tether during its operating life. The preferred tether length is two to five kilometers. The preferred tether mass is one to five percent (1%-5%) of the spacecraft mass. The method of operation comprises orienting the tether structure at a 35.26-degree trailing angle to the local vertical to maximize electrodynamic force on the tether while avoiding tether instability and allowing use of a small tether end mass.
The present invention also teaches that the satellite-tether system may be rotated around its common center of mass to centrifugally produce tension force in the tether structure to oppose forces causing tether instability. The angle of the conductive tether structure of the present invention with respect to the velocity vector of the host spacecraft may be controlled by the method of the present invention so it interacts with the encountered magnetic field to induce a maximum current flow in the tether. This produces maximum electrodynamic drag. All or a portion of this electric power may be stored and then controllably applied to the conductive tether to produce an induced electrodynamic force. This induced electrodynamic force may by used to enhance the drag force, to rotate the tether-satellite system and/or to provide satellite propulsion, i.e. to change the state vector of the satellite for any useful purpose, e.g. to avoid collision or to change the host spacecraft""s orbit to an orbit more favorable for more rapid deorbiting.
The present invention also teaches a tether structure that also functions as a thermal radiator and/or plasma contactor. An embodiment of the present invention using conducting elements of the satellite, e.g. the solar arrays, as electrodynamic tether structures is also disclosed.
The present invention also teaches a method for stabilizing electrodynamic space tethers. Electrodynamic tethers are known to suffer a dynamical instability under operation with constant current or uncontrolled current.i The tether librations, however, can be kept within acceptable bounds by performing feedback control on the tether current.
The key aspects of the method of this embodiment of the present invention are:
Feedback is performed on the in-plane libration (swinging of the tether in the plane defined by the orbital velocity vector and the radius vector).
Feedback is performed by observing the direction of the tether swing. If the tether is swinging in the same direction as the electrodynamic forces, the current in the tether is reduced slightly. A 10% reduction is sufficient. If the tether is swinging in the direction opposite to the electrodynamic forces, the current can be allowed to flow freely.
The control algorithm does not need to know the direction of the electrodynamic force or the magnetic field. All it needs to know is if the tether is performing drag or propulsion. If it is performing drag, then the current is damped when the in-plane swing of the tether is opposite to the orbital motion. If performing propulsion, the current is damped slightly when the tether is swinging forward.
The direction of the tether swing can be deduced from sensor observations on the tether endmass, the host spacecraft, or along the tether itself. One possible method is to use a Global Positioning Satellite receiver to measure and record the velocity of the endmass over time. Periodic variations in the velocity due to tether libration can be observed to determine the direction of tether swing. A second method would be to use accelerometers to observe the acceleration of either the endmass or the host spacecraft. A third method would be to observe the attitude of the endmass or the host spacecraft to deduce the tether libration angle.
The feedback does not eliminate the tether librations. It merely prevents them from growing out of control.
This method is described in more detail and is analyzed in numerical simulations below.